Heat 2 tbsp olive oil in a large pot over medium-high heat. Add 1 lb ground beef, break it up, and cook for 5 minutes until no pink remains. Drain excess fat. Add the diced onion, 3 carrots, and 3 stalks celery and cook for 4 minutes until the onion softens. Add 4 cloves minced garlic and cook 1 more minute.

Stir in 1 tsp oregano, 1 tsp basil, 1/2 tsp thyme, 1/2 tsp red pepper flakes, 1 tsp salt, and 1/2 tsp black pepper. Cook 30 seconds, then pour in 1 can diced tomatoes, 1 can tomato sauce, 4 cups beef broth, and 1 cup water. Scrape up any browned bits from the bottom.

Add the drained kidney beans and cannellini beans. Bring to a boil, then reduce heat to medium-low and simmer uncovered for 15 minutes, stirring occasionally.

Stir in 1 cup dry ditalini pasta, raise heat to medium, and cook for 8 to 10 minutes, stirring every couple of minutes, until the pasta is just tender. Taste and adjust salt.

Ladle into bowls and top with freshly grated Parmesan.